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Rational points on Frey elliptic curves y^2=x^3-n^2x

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Abstract

In this work, we study the rational points on eliptic curves of the form y2 = x3 n2x over finite fields in a different way, i.e. using only elementary number theory. We calculate the number of rational point sover Fp modulo 8. We show that here are two possible cases wherep 1or 3 (mod 4). In the former case we find a classication of the number of points, while in the later case, we know that here are p + 1 points on the curve by the supersingular curve theory.

참고문헌 (14)

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